A class of term structure models with volatility of lognormal type is analyzed in the general HJM framework. The corresponding market forward rates do not explode, and are positive and mean reverting. Pricing of caps and floors is consistent with the Black formulas used in the market. Swaptions are priced with closed formulas that reduce (with an extra assumption) to exactly the Black swaption formulas when yield and volatility are flat. A two-factor version of the model is calibrated to the U.K. market price of caps and swaptions and to the historically estimated correlation between the forward rates.

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

The aim herein is to analyze utility-based prices and hedging strategies. The analysis is based on an explicitly solved example of a European claim written on a nontraded asset, in a model where risk preferences are exponential, and the traded and nontraded asset are diffusion processes with, respectively, lognormal and arbitrary dynamics. Our results show that a nonlinear pricing rule emerges with certainty equivalent characteristics, yielding the price as a nonlinear expectation of the derivative’s payoff under the appropriate pricing measure. The latter is a martingale measure that minimizes its relative to the historical measure entropy. Copyright Springer-Verlag Berlin/Heidelberg 2004Incomplete markets, indifference prices, nonlinear asset pricing,

Abstract. The class of time-decreasing forward performance processes is analyzed in a portfolio choice model of Itô-type asset dynamics. The associated optimal wealth and portfolio processes are explicitly constructed and their probabilistic properties are discussed. These formulae are, in turn, used in analyzing how the investor's preferences can be calibrated to the market, given his desired investment targets.Key words. portfolio choice, forward investment performance, heat equation AMS subject classifications. Primary, 91B16, 91B28DOI. 10.1137/0807452501. Introduction. This paper is a contribution to portfolio management from the perspective of investor preferences and, hence, in its spirit is related to the classical expected utility maximization problem introduced by Merton [8]. Therein, one first chooses an investment horizon and assigns a utility function at the end of it and, in turn, seeks an investment strategy which delivers the maximal expected (indirect) utility of terminal wealth. Recently, we proposed an alternative approach to optimal portfolio choice which is based on the so-called forward performance criterion (see, among others, [10] and [9]). In this approach, the investor does not choose her risk preferences at a single point in time, as is the case in the Merton model, but has the flexibility to revise them dynamically.Herein, we focus on a specific case of a forward performance criterion, originally introduced in [12]. This criterion is a composition of deterministic and stochastic inputs. The deterministic input corresponds to the investor's preferences, or alternatively, to her tolerance towards risk. It is investor specific, represented by a function u (x, t) , which is increasing and concave in x and decreasing in t. The stochastic input, however, is universal for all investors and is given by A t =